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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 37-48 | Cite as

On the Galois Lattice of Bipartite Distance Hereditary Graphs

  • Nicola Apollonio
  • Massimiliano Caramia
  • Paolo Giulio FranciosaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a Bipartite Distance Hereditary graph. We show that the lattice can be realized as the containment relation among directed paths in an arborescence. Moreover, a compact encoding of Bipartite Distance Hereditary graphs is proposed, that allows optimal time computation of neighborhood intersections and maximal bicliques.

Keywords

Galois lattice Transitive reduction Distance hereditary graph Ptolemaic graph 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nicola Apollonio
    • 1
  • Massimiliano Caramia
    • 2
  • Paolo Giulio Franciosa
    • 3
    Email author
  1. 1.Istituto per le Applicazioni del Calcolo M. Picone, CNRRomeItaly
  2. 2.Dipartimento di Ingegneria dell’ImpresaUniversità di Roma “Tor Vergata”RomeItaly
  3. 3.Dipartimento di Scienze StatisticheSapienza Università di RomaRomeItaly

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